We look at functional data as arising from mass spectroscopy data used in proteomics. The data may contain experimental factors and covariates but a desire is to provide interpretation and to discriminate between two or more groups. Modelling is often facilitated by the use of wavelets.
We review a variety of approaches to (i) modelling the functional data as response (ii) modelling directly the discriminatory categories conditional on functional data and experimental factor/covariates. Our ultimate focus will be on Bayesian models that allow regularisation. To this end we look at a variety of forms of scale mixture of normal prior distributions including forms of hyper-lasso and approaches to robustness and stability of discrimination. We are particularly interested in fast algorithms capable of scaling up to very many variables and which are flexible enough to allow a variety of prior structures.
Keywords: Bayesian methods; Hyper-lasso; Bayesian Wavelet functional modelling; MCMC; EM algorithm.